U.S. patent application number 13/031182 was filed with the patent office on 2011-08-25 for method and apparatus for accurately calibrating a spectrometer.
This patent application is currently assigned to USA as Represented by the Administrator of the National Aeronautics and Space Administration. Invention is credited to Stephen M. Simmons, Robert C. Youngquist.
Application Number | 20110208463 13/031182 |
Document ID | / |
Family ID | 44477223 |
Filed Date | 2011-08-25 |
United States Patent
Application |
20110208463 |
Kind Code |
A1 |
Youngquist; Robert C. ; et
al. |
August 25, 2011 |
Method and Apparatus for Accurately Calibrating a Spectrometer
Abstract
A calibration assembly for a spectrometer is provided. The
assembly includes a spectrometer having n detector elements, where
each detector element is assigned a predetermined wavelength value.
A first source emitting first radiation is used to calibrate the
spectrometer. A device is placed in the path of the first radiation
to split the first radiation into a first beam and a second beam.
The assembly is configured so that one of the first and second
beams travels a path-difference distance longer than the other of
the first and second beams. An output signal is generated by the
spectrometer when the first and second beams enter the
spectrometer. The assembly includes a controller operable for
processing the output signal and adapted to calculate correction
factors for the respective predetermined wavelength values assigned
to each detector element.
Inventors: |
Youngquist; Robert C.;
(Cocoa, FL) ; Simmons; Stephen M.; (Melbourne,
FL) |
Assignee: |
USA as Represented by the
Administrator of the National Aeronautics and Space
Administration
Washington
DC
|
Family ID: |
44477223 |
Appl. No.: |
13/031182 |
Filed: |
February 19, 2011 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61307985 |
Feb 25, 2010 |
|
|
|
Current U.S.
Class: |
702/104 |
Current CPC
Class: |
G01J 3/0208 20130101;
G01J 3/28 20130101; G01J 3/02 20130101; G01J 3/021 20130101 |
Class at
Publication: |
702/104 |
International
Class: |
G06F 19/00 20110101
G06F019/00; G01J 3/00 20060101 G01J003/00 |
Claims
1. A calibration assembly for a spectrometer, the assembly
comprising: a spectrometer having first and second detector
elements, the first and second detector elements being assigned
predetermined respective first and second wavelength values; a
first source emitting a first radiation for calibrating the
spectrometer; a device placed in the path of the first radiation to
split the first radiation into a first beam and a second beam;
wherein one of the first and second beams travels a path-difference
distance longer than the other of the first and second beams;
wherein the spectrometer is configured to generate an actual output
signal when the first beam and the second beam enter the
spectrometer; a controller operable for processing the actual
output signal; and wherein the controller is adapted to calculate
first and second correction factors for the respective first and
second wavelength values by comparing the actual output signal with
a theoretically-predicted output signal.
2. The assembly of claim 1, further comprising: a first mirror
positioned such that the first beam travels a first distance to the
first mirror to be reflected towards the spectrometer; a second
mirror positioned such that the second beam travels a second
distance to the second mirror to be reflected towards the
spectrometer; and wherein the device placed in the path of the
first radiation is a beam splitter.
3. The assembly of claim 1, further comprising: a first lens
adapted to collimate the first radiation emitted by the source
prior to the first radiation entering the beam splitter; and a
second lens adapted to collimate the first and second beams prior
to the first and second beams entering the spectrometer.
4. The assembly of claim 1, further comprising: a first blocking
device to selectively block the first beam; a second blocking
device to selectively block the second beam; wherein the
spectrometer is configured to generate a reference signal when the
first beam is selectively blocked and the second beam enters the
spectrometer; and wherein the spectrometer is configured to
generate a dark signal when the first beam and the second beam are
selectively blocked from entering the spectrometer.
5. The assembly of claim 4, further comprising: an algorithm stored
on the controller; wherein the algorithm determines a
dark-corrected reference signal by subtracting the dark signal from
the reference signal; wherein the algorithm determines a
dark-corrected output signal by subtracting the dark signal from
the output signal; wherein the algorithm determines an actual
normalized output by dividing the dark-corrected output signal by
the dark-corrected reference signal.
6. The assembly of claim 5, wherein: the algorithm correlates the
actual normalized output with a first correlation function to
determine a first function; and the algorithm determines a
first-approximation for the path-difference distance occurring at a
maximum value for the first function.
7. The assembly of claim 6, wherein: the algorithm adds an
integration correction factor to the first function to obtain a
second function; and the algorithm determines the path-difference
distance between the first beam and the second beam, the
path-difference distance occurring at a maximum value for the
second function.
8. The assembly of claim 7, wherein: the algorithm multiplies the
predicted normalized output with a predetermined ideal function to
generate a third function having an oscillatory term and a drift
term; and the algorithm filters out the oscillatory term; wherein
the algorithm calculates respective preliminary first and second
correction factors for the respective first and second wavelength
values.
9. The assembly of claim 8, further comprising: a second source
configured to emit second radiation having at least one
known-wavelength, the second radiation generating a signal at a
detected-wavelength at the spectrometer; wherein the algorithm
calculates a fixed-offset error by comparing the
detected-wavelength with the known-wavelength; and wherein the
algorithm calculates the first and second correction factors for
the respective first and second wavelength values by applying the
fixed-offset error to the preliminary first and second correction
factors.
10. A method of calibrating a spectrometer having first and second
detector elements, the method comprising: assigning pre-determined
first and second wavelength values to the first and second detector
elements; illuminating the spectrometer with a first radiation
emitted by a first source; splitting the first radiation into a
first beam and a second beam such that one of the first and second
beams travels a path-difference distance longer than the other of
the first and second beams; generating an actual output signal at
the spectrometer when the first beam and the second beam enter the
spectrometer; and calculating first and second correction factors
for the first and second wavelength values by comparing the actual
output signal with a theoretically-predicted output signal.
11. The method of claim 10, further comprising: selectively
blocking the first beam with a first blocking device; selectively
blocking the second beam with a second blocking device; generating
a dark signal at the spectrometer when both the first beam and
second beam are blocked; generating a reference signal at the
spectrometer when one of the first and second beams is blocked;
subtracting the dark signal from the actual output signal to
produce a dark-corrected output signal; subtracting the dark signal
from a reference signal to produce a dark-corrected reference
signal; and dividing the dark-corrected output signal by the
dark-corrected reference signal to produce an actual normalized
output.
12. The method of claim 11, further comprising: correlating the
actual normalized output with a first correlation function to
determine a first function; and determining a first-approximation
for the path-difference distance occurring at a first maximum value
of the first function.
13. The method of claim 12, further comprising: adding an
integration correction factor to the first function to obtain a
second function; and determining the path-length difference between
the first beam and the second beam, the path-difference distance
occurring at a second maximum value of the second function.
14. The method of claim 13, further comprising: multiplying the
predicted normalized output with a predetermined ideal function to
generate a third function having an oscillatory term and a drift
term; filtering out the oscillatory term; and calculating a
preliminary first correction factor for the first wavelength value
and a preliminary second correction factor for the second
wavelength value.
15. The method of claim 14, further comprising: configuring a
second source to emit second radiation having at least one
known-wavelength, wherein the second radiation generates a signal
at a detected-wavelength at the spectrometer; calculating a
fixed-offset error by comparing the detected-wavelength with the
known-wavelength; and calculating the first and second correction
factors for the respective first and second wavelength values
respectively by applying the fixed-offset error to the respective
preliminary first and second correction factors.
16. A calibration assembly for a spectrometer, the assembly
comprising: a spectrometer having a plurality of detector elements,
wherein each of the plurality of detector elements is assigned a
respective one of a plurality of wavelength values; a first source
emitting first radiation; a beam splitter placed in the path of the
first radiation to split the first radiation into a first beam and
a second beam; wherein one of the first and second beams travels a
path-difference distance longer than the other of the first and
second beams; a first blocking device to selectively block the
first beam; a first mirror positioned such that the first beam
travels a first distance to the first mirror, the first beam being
reflected towards the spectrometer; a second mirror positioned such
that the second beam travels a second distance to the second
mirror, the second beam being reflected towards the spectrometer;
an actual output signal generated by the spectrometer when the
first beam and the second beam are incident on the spectrometer; a
reference signal generated by the spectrometer when the first beam
is selectively blocked; a controller operable for processing the
actual output signal and the reference signal; and wherein the
controller is adapted to calculate a plurality of correction
factors for each of the respective plurality of wavelength values
by comparing the actual output signal with a
theoretically-predicted output signal.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application claims the benefit under 35 U.S.C.
.sctn.119(e) of U.S. Provisional Application Ser. No. 61/307,985,
filed Feb. 25, 2010, the contents of which are incorporated herein
by reference.
ORIGIN OF THE INVENTION
[0002] The invention described herein was made in the performance
of work under a NASA contract and by an employee of the United
States Government and is subject to the provisions of Public Law
96-517 (35 U.S.C. .sctn.202) and may be manufactured and used by or
for the Government for governmental purposes without the payment of
any royalties thereon or therefor. In accordance with 35 U.S.C.
.sctn.202, the contractor elected not to retain title.
TECHNICAL FIELD
[0003] The present invention relates generally to calibration of an
optical instrument, and more particularly, to a method and
apparatus for calibration of a spectrometer.
BACKGROUND OF THE INVENTION
[0004] A typical spectrometer includes a plurality of detector
elements. When the spectrometer is illuminated with radiation
having multiple wavelengths, each detector element records an
intensity factor for a particular wavelength. The wavelength
assignment of each detector element should be the value of the
particular wavelength that reaches that detector after passing
through the spectrometer optics. In order to determine the
wavelength assignment of each detector element, the spectrometer is
calibrated using a source that emits radiation at a few known
wavelength points in the spectrum. The spectrometer receives the
radiation and records an intensity value for the known wavelength
points. In order to determine the wavelength assigned to each
detector element, a functional fit or polynomial fit is performed
to interpolate points within the spectrum and extrapolate points
outside the spectrum. However, the wavelength assignments obtained
by this method of calibration are typically accurate only to
approximately one nanometer.
SUMMARY OF THE INVENTION
[0005] A calibration assembly for a spectrometer is provided. The
assembly includes a spectrometer having first and second detector
elements, the first detector element being assigned a predetermined
first wavelength value and the second detector element being
assigned a predetermined second wavelength value. A first source
emitting first radiation is used to calibrate the spectrometer. A
device is placed in the path of the first radiation to split the
first radiation into a first beam and a second beam. The assembly
is configured so that one of the first and second beams travels a
path-difference distance longer than the other of the first and
second beams. An actual output signal is generated by the
spectrometer when the first and second beams enter the
spectrometer. The assembly includes a controller operable for
processing the actual output signal. The controller is adapted to
calculate first and second correction factors for the respective
first and second wavelength values by comparing the actual output
signal with a theoretically-predicted output signal.
[0006] The calibration assembly allows for wavelength values of
each detector element to be determined to within approximately 0.01
nanometers. In a spectrometer having a plurality of detector
elements, the calibration assembly allows for each detector element
to be calibrated, as opposed to calibrating a few detector elements
and interpolating values for the rest of the detector elements as
is conventionally done.
[0007] The above features and advantages and other features and
advantages of the present invention are readily apparent from the
following detailed description of the best modes for carrying out
the invention when taken in connection with the accompanying
drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] FIG. 1 is a schematic diagram of a calibration assembly for
the calibration of a spectrometer;
[0009] FIG. 2 is a graph illustrating an example of signal received
from the spectrometer of FIG. 1;
[0010] FIG. 3 is a graph illustrating an example of an intermediate
function determined according to an algorithm stored in the
controller of the calibration assembly of FIG. 1;
[0011] FIG. 4 is a graph illustrating an example of preliminary
correction factors determined according to the algorithm stored in
the controller of the calibration assembly of FIG. 1; and
[0012] FIG. 5 is a flow chart describing the algorithm for the
calibration of the spectrometer shown in FIG. 1; and
[0013] FIG. 6 is a schematic diagram of a second source of
radiation used for the calibration of the spectrometer shown in
FIG. 1.
DETAILED DESCRIPTION OF THE INVENTION
[0014] Referring to the drawings, wherein like reference numbers
correspond to like or similar components throughout the several
figures, a calibration assembly 10 is shown in FIG. 1. The assembly
10 includes a spectrometer 14 that is to be calibrated using first
radiation 12. A first source 16 for generating the first radiation
12 is shown in FIG. 1. The first radiation 12 may be
electromagnetic radiation covering the visible spectrum, also known
as white light. Alternatively, the first radiation 12 may be
broadband radiation, defined here as covering the entire spectrum
that the spectrometer 14 has the ability to process. The first
source 16 may be operatively connected to a first fiber optic 18 to
carry the first radiation 12 away from the first source 16. Any
other method of sending and receiving the first radiation 12 may be
employed.
[0015] Referring to FIG. 1, a device such as a beam splitter 22 is
placed in the path of the first radiation 12 to split the radiation
into a first beam 24 and a second beam 26. The first beam 24
travels a first distance 28 to a first mirror 30. The first beam 24
is then reflected from the first mirror 30 and re-enters the beam
splitter 22, as shown by arrow 32. The first beam 24 passes through
the beam splitter 22 and subsequently enters the spectrometer 14,
as shown by arrow 34. The second beam 26 travels a second distance
36 to a second mirror 38. The second beam 26 is then reflected from
the second mirror 38 and re-enters the beam splitter 22, as shown
by arrow 40. The second beam 26 passes through the beam splitter 22
and subsequently enters the spectrometer 14, as shown by arrow 42.
The spectrometer 14 records intensity from the first beam 24 and
the second beam 26 over a range of wavelengths thereby generating
an output signal 210 (described below and shown in FIG. 2). A
second fiber optic 44 may be connected to the spectrometer 14 to
transport the first and second beams 24, 26 to the spectrometer
14.
[0016] The assembly 10 is configured so that the first beam 24
travels a longer distance than the second beam 26 (or vice-versa).
The path-difference distance d is defined as the round-trip
difference in distance traveled between the first beam 24 and
second beam 26. In other words, the distance d is twice the first
distance 28 minus twice the second distance 36 (or vice-versa if
the second distance 36 is longer than the first distance 28). The
first beam 24 may be selectively blocked from entering the
spectrometer 14 by a first blocking device 46, shown in FIG. 1. The
second beam 26 may be selectively blocked from entering the
spectrometer 14 by a second blocking device 47, shown in FIG. 1. A
first lens 48 may be used to collimate or focus the first radiation
12 leaving the first source 16, prior to being incident on the beam
splitter 22. A second lens 49 may be used to collimate or focus the
first and second beams 24, 26 exiting the beam splitter 22. The
type of first radiation 12 and beam-splitter 22 can be selected by
one of ordinary skill in the art, depending on the type of
spectrometer 14 being calibrated and other factors.
[0017] The spectrometer 14 includes n detector elements or pixels
that are each sensitive to a wavelength .lamda..sub.i, where i=1 .
. . n. A spectrometer 14 with any number of detector elements may
be employed. For illustration purposes, the spectrometer 14 is
described with respect to two of the n detector elements, a first
detector element 50 and a second detector element 52. The first
detector element 50 is assigned a first wavelength value
.lamda..sub.1 and the second detector element 52 is assigned a
second wavelength value .lamda..sub.2. The first and second
wavelength values .lamda..sub.1, .lamda..sub.2 may be available
from the manufacturer of the spectrometer 14, as is readily
understood by persons of ordinary skill in the art. Alternatively,
the first and second wavelength values .lamda..sub.1, .lamda..sub.2
may be determined by conventional calibration techniques involving
a source with emissions having known wavelength. A functional fit
or polynomial fit is performed to interpolate or extrapolate points
outside of the known wavelength, as readily understood by persons
of ordinary skill in the art.
[0018] Referring to FIG. 1, a controller 70 is included in the
assembly 10. Controller 70 executes an algorithm 100 which resides
within the controller 70 or is otherwise readily executable by the
controller 70. FIG. 5 is a flow chart showing the algorithm 100.
The controller 70 is adapted to calculate first and second
correction factors 54, 56 (shown in step 120 of FIG. 5) for the
first and second wavelength values .lamda..sub.1,.lamda..sub.2. The
controller 70 is adapted to process the output of the spectrometer
14 (steps 102, 104, 106, and 108 of FIG. 5). The controller 70 may
be a general-purpose digital computer, a microprocessor, central
processing unit, or a computer-readable storage medium.
Part 1--Obtaining an Actual Normalized Output
[0019] When the first radiation 12 enters the spectrometer 14, a
signal intensity is detected at each detector element n. FIG. 2 is
a graph illustrating an example of a signal received from the
spectrometer 14. The x-axis 202 represents wavelength in nanometers
and the y-axis 204 represents intensity in arbitrary units. In this
case, the output from the spectrometer 14 was integrated over 2-3
milliseconds and the measurement repeated every 3 seconds. The time
for repeating the measurement and integration of signal may be
varied according to the particular application. The signal received
will differ depending on the type of source, beam-splitting device,
and spectrometer used.
[0020] Referring to FIG. 2, a dark signal 206 is obtained when both
the first and second beams 24, 26 are blocked. The dark signal 206
represents the background noise of the system. A reference signal
208 is obtained when the first beam 24 is blocked and the second
beam 26 is transmitted to the spectrometer 14. Alternatively, the
second beam 26 may be blocked and the first beam 24 is transmitted
to the spectrometer 14. An output signal 210 is obtained when both
the first beam 24 and second beam 26 are received at the
spectrometer 14. The output signal 210 is oscillatory as a result
of interference of the first and second beams 24, 26 traveling
along different paths.
[0021] Referring to FIG. 5, the algorithm 100 begins with step 102,
where the controller 70 receives the output signal 210, reference
signal 208 and dark signal 206. At step 104, the controller 70
determines a dark-corrected reference signal 103 by subtracting the
dark signal 206 from the reference signal 208. At step 106, the
controller 70 determines a dark-corrected output signal 105 by
subtracting the dark signal 206 from the output signal 210. At step
108, the controller 70 determines an actual normalized output 107
by dividing the dark-corrected output signal 105 by the
dark-corrected reference signal 103.
[0022] The actual normalized output 107 for the first and second
detectors 50, 52 is represented by the array [P(.lamda..sub.1),
P(.lamda..sub.2)], which is data obtained at the spectrometer 14.
The actual normalized output 107 determined above is compared to a
theoretically predicted normalized output 109. The predicted
normalized output 109 for the first and second detectors 50, 52 is
assumed to be represented by the array
[(1+cos(2.pi.d/.lamda..sub.1)), (1+cos(2.pi.d/.lamda..sub.2))],
where d is the path-difference distance between the first and
second beams 24, 26. It is assumed that the difference between the
predicted normalized output 109 and the actual normalized output
107 obtained by the spectrometer 14 represents wavelength
assignment errors. This difference is used to calculate the first
and second correction factors 54, 56 for the first and second
wavelength values X.sub.1, X.sub.2, respectively.
Part 2--Correlation Process To Determine Path-Difference
Distance
[0023] In order for the controller 70 to obtain the first and
second correction factors 54, 56, a determination of the
path-difference distance d is required. A correlation process
described below is carried out to determine the path-difference
distance d. An alternative method to determine the path-difference
distance d may be substituted.
[0024] At step 110, the controller 70 correlates the actual
normalized output 107 with a first correlation function represented
by the array [(cos(2.pi.z/.lamda..sub.1))/.lamda..sub.1,
(cos(2.pi.z/.lamda..sub.2))/.lamda..sub.2], having a variable
parameter z. The correlation process is as follows: the actual
normalized output 107 is multiplied by the first correlation
function and integrated for all detector elements to obtain a first
function 111. For a system with n detectors, the first function 111
is
.SIGMA..sub.i-1 to
nP(.lamda..sub.i)cos(2.pi.z/.lamda..sub.i)(.DELTA..lamda..sub.i/.lamda..s-
ub.i),
where the P(.lamda..sub.i) are the n spectral power measurements
obtained from the normalization process described in step 108. The
predicted normalized output 109 for the first and second detectors
50, 52, represented by the array [(1+cos(2.pi.d/.lamda..sub.1)),
(1+cos(2.pi.d/.lamda..sub.2))], is then plugged into the first
function 111. The controller 70 then determines a peak value or
maximum value for the first function 111, which occurs when the
variable parameter z is equal to d. This is readily understood by
one of ordinary skill in the art since the first function 111 will
have a square of a cosine parameter when z is equal to d (the
square of a cosine is always 1, whereas a cosine is always between
-1 and 1 (inclusive); thus the square of a cosine is always greater
than or equal to a cosine). The value of d determined here is a
first-approximation of the path-difference distance because the
range of integration is finite. In other words, the range of
integration is limited to the shortest, .lamda..sub.1, and the
longest wavelengths, .lamda..sub.n, that have significant
signal.
[0025] At step 112, the controller 70 adds an integration
correction factor to the first function 111 to obtain a second
function 113. For a system with i=1 . . . n detectors, the second
function 113 is:
.SIGMA..sub.i-1 to
nP(.lamda..sub.i)cos(2.pi.z/.lamda..sub.i)(.DELTA..lamda..sub.i/.lamda..s-
ub.i)-[Ci(2.pi.z/.lamda..sub.1)-Ci(2.pi.z/.lamda..sub.n]-[Ci(4.pi.z/.lamda-
..sub.1)-Ci(4.pi.z/.lamda..sub.n)]/4,
where the P(.lamda..sub.i) are the n spectral power measurements
obtained from the normalization process described in step 108. In
the second function 113, Ci is the cosine integral function which
is readily understood by those of ordinary skill in the art. The
second function 113 is adapted to correct for integration errors.
The correlation process described above is repeated with the second
function 113, using the approximate value for d as a starting
point. The controller 70 searches for a peak or maximum value of
the second function 113, which occurs when the variable parameter z
is equal to the correct path-difference d. Thus a value of the
path-difference distance d is determined.
Part 3--Using Path-Difference Distance to Determine Preliminary
Correction Factors
[0026] Using the path-difference distance d determined in step 112,
a preliminary first correction factor 58 (.eta..sub.1) for the
first wavelength value .lamda..sub.1 and a preliminary second
correction factor 60 (.eta..sub.2) for the second wavelength value
.lamda..sub.2 may be obtained. The preliminary first and second
correction factors 58, 60 [.eta..sub.1,.eta..sub.2] are related to
the first and second correction factors 54, 56 (the relationship is
described in step 120 below).
[0027] In step 114, the controller 70 multiplies the cosine portion
[cos(2.pi.d/.lamda..sub.1), cos(2.pi.d/.lamda..sub.2)] of the
predicted normalized output 109 with an ideal function
[sin(2.pi.d.lamda..sub.1/(.lamda..sub.1+.eta..sub.1)),
sin(2.pi.d.lamda..sub.2/(.lamda..sub.2+.eta..sub.2))], resulting in
the generation of a third function 115. As noted above, the
predicted normalized output 109 for the first and second detectors
50, 52 is represented by the array [(1+cos(2.pi.d/.lamda..sub.1)),
(1+cos(2.pi.d/.lamda..sub.2))], where d is the path-difference
distance between the first and second beams 24, 26. For a system
with i=1 . . . n detectors, the third function 115 can be
represented as:
{cos(2.pi.d/.lamda..sub.i).
sin(2.pi.d.lamda..sub.i/(.lamda..sub.i+.eta.))},
which is approximately equal to
{-(1/2)sin(2.pi.d.eta..sub.i/.lamda..sub.i.sup.2)+(1/2)sin(4.pi.d/.lamda.-
.sub.i)}. The third function 115 includes a high-frequency
oscillatory term 117 ((1/2)sin(4.pi.d/.lamda..sub.i)). The term
(-(1/2)sin(2.pi.d.eta..sub.i/.lamda..sub.i.sup.2)) is a drift term.
FIG. 3 is a graph illustrating an example 220 of a third function
115 having both an oscillatory term 117 and a drift term, as
described above. The x-axis 222 represents wavelength in nanometers
and the y-axis 224 represents arbitrary units.
[0028] In step 116, the oscillatory term 117
((1/2)sin(4.pi.d/.lamda..sub.i)) is averaged out or filtered out,
leaving only the drift term
(-(1/2)sin(2.pi.d.eta..sub.i/.lamda..sub.i.sup.2)). Techniques for
averaging out oscillatory terms are known to those of ordinary
skill in the art. For example, digital filtering methods, Fourier
transformation methods or sliding filter methods may be used. In
the sliding filter method, adjacent maximum and minimum values are
averaged out and this is repeated for each point in the spectrum.
Any suitable method for filtering out the oscillatory terms may be
used. Since the path-difference distance d is known from step 112,
the preliminary first and second correction factors 58, 60
[.eta..sub.1,.eta..sub.2] can be determined.
[0029] In step 118, the preliminary first and second correction
factors 58, 60 [.eta..sub.1, .eta..sub.2] determined in step 116
are applied to the first and second wavelength values
.lamda..sub.1, .lamda..sub.2 and steps 110, 112, 114 and 116 are
repeated. A revised preliminary first correction factor 58
(.eta..sub.1) and a revised preliminary second correction factor 60
(.eta..sub.2) is generated.
[0030] FIG. 4 is a graph illustrating an example of preliminary
correction factors 58, 60 that were calculated by the controller 70
for the spectrometer 14. The x-axis 232 represents wavelength in
nanometers and the y-axis 234 represents preliminary correction
factor in nanometers. The preliminary correction factor varies for
each detector element (assigned to a particular wavelength). A
first-approximation trace 236 shows preliminary correction factors
obtained in accordance with step 116. The first-approximation trace
236 shows a maximum preliminary correction factor of approximately
1.5 nanometers, at the detector element assigned to about 850
nanometers. A second-approximation trace 238 shows preliminary
correction factors obtained in accordance with step 118, in other
words, repeating steps 110, 112, 114, and 116. As shown in FIG. 4,
the preliminary correction factors in the second-approximation
trace 238 are less than 0.01 nanometers in magnitude across the
spectrum. Thus the algorithm 100 allows for wavelength values to be
corrected to within approximately 0.01 nanometers.
Part 4--A Fixed-Offset Correction to Obtain Correction Factors
[0031] A next step may be employed to further refine the
preliminary first and second correction factors 58, 60
[.eta..sub.1,.eta..sub.2]. Because the above calculations involve a
normalization and smoothing process, the first and second
wavelength values .lamda..sub.1, .lamda..sub.2 may be biased in one
direction or another, either too large or too small. A fixed-offset
error 119 is calculated to compensate for this effect. The
fixed-offset error 119 may be described by the function
[1/(1+.delta.)], where .delta. may be a positive or negative
number. The fixed-offset error 119 may be calculated using a source
with at least one known wavelength. A suitable alternative for
finding the fixed-offset error 119 may be substituted.
[0032] The corrected wavelength value for n detector elements can
be represented by (.lamda..sub.i+.epsilon..sub.i), where i=1 . . .
n. In step 120, the controller 70 calculates the first and second
correction factors [.epsilon..sub.1, .epsilon..sub.2] for the first
and second wavelength values [.lamda..sub.1, .lamda..sub.2] of the
first and second detector elements 50, 52, respectively. The first
and second correction factors 54, 56 [.epsilon..sub.1,
.epsilon..sub.2] are determined by applying the fixed-offset error
(1/(1+.delta.)) to the preliminary first and second correction
factors 58, 60 [.eta..sub.1, .eta..sub.2. The relationship can be
represented by:
(.lamda..sub.i+.epsilon..sub.i=(.lamda..sub.i+.eta..sub.i)/(1+.delta.)).
Simplifying this further results in:
(.epsilon..sub.i=.eta..sub.i-.delta..lamda..sub.i). Therefore the
first and second correction factors 54, 56 [.epsilon..sub.1,
.epsilon..sub.2] are
[.eta..sub.1-.delta..lamda..sub.1,.eta..sub.2-.delta..lamda..sub.2].
The preliminary first and second correction factors 58, 60
[.eta..sub.1,.eta..sub.2] were determined previously.
[0033] Referring to FIG. 6, the .delta. factor is calculated using
a second source 80 configured to emit second radiation 82 having a
known-wavelength .lamda..sub.known. FIG. 6 is a schematic diagram
of the second source 80. For example, the second source 80 may be a
laser with emissions centered around one known wavelength. The
second radiation 82 from the second source 80 enters the
spectrometer 14 and a peak is detected at a detected-wavelength
.lamda..sub.detected. The .delta. factor is calculated by comparing
the known-wavelength .lamda..sub.known and the detected-wavelength
.lamda..sub.detected since .lamda..sub.known=.lamda..sub.detected
(1/(1+.delta.)).
[0034] While the best modes for carrying out the invention have
been described in detail, those familiar with the art to which this
invention relates will recognize various alternative designs and
embodiments for practicing the invention within the scope of the
appended claims.
* * * * *